Forecasting - 3 Demand Pooling Ardavan Asef-Vaziri Based on Operations management: Stevenson Operations Management: Jacobs, Chase, and Aquilano Supply Chain Management: Chopra and Meindl. Chapter 7 Demand Forecasting in a Supply Chain. Aggregate Demand.
Forecasting - 3 Demand Pooling ArdavanAsef-Vaziri Based on Operations management: Stevenson Operations Management: Jacobs, Chase, and Aquilano Supply Chain Management: Chopra and Meindl Chapter 7Demand Forecastingin a Supply Chain
Aggregate Demand • A firm produces Red and Blue T-Shirts. How much safety stock
Forecasts and Probability Distributions • Suppose the company stocks 956 T-shirts, the forecasted number. What is the probability the company will have a stockout, that is, that there will not be enough T-shirts to satisfy demand? • The company does not want to have unsatisfied demand, as that would be lost revenue. So the company overstocks. Suppose the company stocks 1,026 units. • What is the probability that the actual demand will be larger than 1,026?
There is a Distribution Around the Forecasted Sale Standard Deviation of Error = 1.25 MAD • Error is assumed to NORMALLY DISTRIBUTED with • A MEAN (AVERAGE) = 0 • STANDARD DEVIATION = 1.25* MAD
How many to stock Suppose the company desires that the probability of not being able to meet demand is 2.5% Look-up on normal table (show using book)
Blue Product Inventory Level • The stocking level, of the blue product, for period 11 is: 987+1.96*(1.25*410)=1991 • Recall that: amt. stocked = forecast + 1.96x1.25xMAD implies the probability of not satisfying demand is P( demand > amt. stocked ) = 0.025.
Total Inventory Level • The total inventory for Red and Blue is: 1892 + 1728 = 3620 • P( Red demand > # of Red T-shirts stocked ) = 0.025 P( Blue demand > # of Blue T-shirts stocked ) = 0.025
Aggregate Forecasts • Can we more accurately forecast the combined demand? • Suppose we can make Gray Shirt and then dye the T-shirts either red or blue. • What is the Demand for Gray Shirts? • We look at the sum of the demands in the past • We forecast the demand for the two products combined • We compute the MAD for the aggregate forecast
Forecast for the Aggregate Demand Inventory of Gray = 1942 + 1.96*1.25*717 = 3699 Compared to 3883
Aggregate Demand Forecast Conclusions • By stocking 3699 Gray T-shirts, we ensure P( T-shirt demand > # stocked ) = 0.025 • Otherwise, we needed to stock 1892 blue T-shirts and 1991 red T-shirts for a combined number of 1892+1991 = 3883 T-shirts to ensure that P( red T-shirt demand > # red shirts stocked) = P( blue T-shirt demand > # blue shirts stocked) = 0.025 • 3699 < 3883 … we need to stock less T-shirts to ensure a given stockout probability (2.5% in this example) when we have an aggregate forecast.